[pinterbanget]

Summary

This adds research/gate-existence-check/. It is an independent certified recomputation of the finite figures in dillona's #4532 (adaptive gates at a moment crossing), the compiler that #4535's κ = 0.003020165 rests on.

Claim type: an independent certified recomputation. No new κ.

Results

All of #4532's tables reproduce.

• Abstract witness (T(1/2) = P(1/2) = 68): mean gap 4.765 ≥ 4; U = 0.6223559 < .622356; V = 0.6603487 < .660349; mirror 0.010664 ≤ 1/80 < capacity 1/32; tangent cover holds; recurrence bound 272.8579195 > 272.857919, against the required 155/3.

• Counterexample. T(1/2 − λ)e^{λμ_P} = 8 + 136·16^{−λ} > 8 = P(1/2) for every λ > 0, and the mirror ratio is exactly 1/17 < 1/16.

• Root applications:

  	gap	mirror	capacity	D	required
  p7	1.723542	.320851	.984544	.028590	.023329
  p16	1.042285	.562814	.982102	.048546	.042808

  The guards also hold on the critical covers.

Evidence

python3.12 -B scripts/research_package.py --package research/gate-existence-check --check-only
  PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
python3.12 -B scripts/research_package.py --package research/gate-existence-check
  PASS_REGISTERED_RESEARCH_PACKAGE research/gate-existence-check outcome=completed   (~25 s, stdlib only)

Head: 530a5b6d2ae7ee0a1eccc88975a170cf39b60b94. Base: canonical main f9f85c1e.

Not covered

• Prove adaptive gate criterion and critical-root leaf bounds (no κ) #4532's theorem itself: the integral identities, the existence argument and the critical-endpoint majorant.

Credit: dillona (#4532) and zxv (#4483). Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.

🤖 Generated with Claude Code